Tilted Special Biserial Algberas François Huard and Shiping Liu ...

We shall now find some sufficient conditions for a string module to be of
projective dimension greater than one. Note that each reduced walk w in a
quiver can be uniquely written as w = p −1
1 q 1 ···p −1
n q n,wheren ≥ 1, the p i and
the q j are paths which are non-trivial for 1